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[Mentors note: Thread moved from the Classical Physics forum after it had been replied to, hence the lack of a homework template]

Hey I have been trying to solve this problem for the last few days with no luck.

Question:

a car starts from rest at the origin and travels along the path given by y=0.2 x ^(3/2) and picking up speed in accordance with v = 4.8 t. At which x position does the car skid off the path? Friction force is known as well (Ff)

Attempt at answer:

I parametrized the curve in terms of time, r(t) = <t, 0.2t^3/2> , calculated the radius of curvature (R) as a function of t, and used this to solve for the centripetal force using Fc = mv^2 / R , where v=4.8t . Then I said that the force of friction always acts in the inward normal direction to keep the car from going off the path. The road exerts a reaction force on the vehicle equal to - Fc . Therefore using newtons second law i solved for the position t when Fc = Ff. This all makes sense to me although Ive been told this is not the correct method. Any thoughts are appreciated. Thanks

Hey I have been trying to solve this problem for the last few days with no luck.

Question:

a car starts from rest at the origin and travels along the path given by y=0.2 x ^(3/2) and picking up speed in accordance with v = 4.8 t. At which x position does the car skid off the path? Friction force is known as well (Ff)

Attempt at answer:

I parametrized the curve in terms of time, r(t) = <t, 0.2t^3/2> , calculated the radius of curvature (R) as a function of t, and used this to solve for the centripetal force using Fc = mv^2 / R , where v=4.8t . Then I said that the force of friction always acts in the inward normal direction to keep the car from going off the path. The road exerts a reaction force on the vehicle equal to - Fc . Therefore using newtons second law i solved for the position t when Fc = Ff. This all makes sense to me although Ive been told this is not the correct method. Any thoughts are appreciated. Thanks

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